Tube configuration for a heat exchanger, heat exchanger including the tube configuration, fluid heating system including the same, and methods of manufacture thereof

ABSTRACT

A heat exchanger tube assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter wherein adjacent tubes on the same ring are separated by a fixed radial separation angle and adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of U.S. Provisional Patent Application Ser. No. 62/268,099 filed Jan. 22, 2016, and U.S. Provisional Patent Application Ser. No. 62/360,711 filed Jul. 11, 2016. The related applications are incorporated herein in their entirety by reference.

BACKGROUND

(1) Field

This disclosure relates to fluid heating systems using shell and tube heat exchangers.

(2) Description of the Related Art

Fluid heating systems, including steam, hydronic (water), and thermal fluid boilers, constitute a broad class of devices for producing a heated fluid for use in domestic, industrial, and commercial applications. Because of the desire for improved energy efficiency, compactness, reliability and cost reduction, there remains a need for improved fluid heating systems, as well as improved methods of manufacture thereof.

SUMMARY

Disclosed is a heat exchanger tube assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter wherein adjacent tubes on the same ring are separated by a fixed radial separation.

Also disclosed is a heat exchanger tube assembly comprising a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, and adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring.

Also disclosed is a heat exchanger comprising: a pressure vessel; a heat exchanger tube assembly disposed in the pressure vessel, the tube assembly comprising a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA.

Also disclosed is a heat exchanger comprising: a pressure vessel; a heat exchanger tube assembly disposed in the pressure vessel, the tube assembly comprising a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA, and adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring.

Also disclosed is a fluid heating system comprising: a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a heat exchanger tube assembly disposed in the pressure vessel shell, the heat exchanger tube assembly comprising, a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Also disclosed is a fluid heating system comprising: a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a heat exchanger tube assembly disposed in the pressure vessel shell, the heat exchanger tube assembly comprising, a first tube sheet, a second tube sheet opposite the first sheet, a plurality of heat exchanger tubes, each independently connects the first tube sheet and the second tube sheet, wherein the tubes are in a staggered ring configuration that comprises a concentric sequence of rings of decreasing diameter and wherein adjacent tubes on the same ring are separated by a fixed radial separation angle, RA, and wherein adjacent tubes on adjacent rings are staggered by rotating all the tubes within an inner ring by a fixed radial index angle, IA, relative to the next outermost tube ring; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Also disclosed is a method for computing the radial separation angle and the radial stagger index angle for a staggered ring heat exchanger tube configuration, using the design diameter of the tube configuration, the required gap between the design diameter and the first tube ring, the tube element clearance diameter required for each ring of tubes, and the rounding threshold to be applied to the tube count calculation.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee.

The above and other advantages and features of this disclosure will become more apparent by describing in further detail exemplary embodiments thereof with reference to the accompanying drawings, in which:

FIG. 1 is a schematic diagram of an embodiment of a fluid heating system which includes an embodiment of a combustion gas supply system;

FIG. 2 shows a perspective view of an embodiment of a shell-and-tube heat exchanger incorporating baffles to induce radial production fluid flow;

FIG. 3 is a perspective rendering of an embodiment of a shell-and-tube heat exchanger incorporating an alternating plate and annular baffle assembly and illustrating the radial flow created by the baffle assembly;

FIG. 4 provides a flow diagram for a method to compute the radial separation angle and the radial stagger index angle for a staggered ring heat exchanger tube configuration, using the design diameter of the tube configuration, the required gap between the design diameter and the first tube ring, the tube element clearance diameter required for each ring of tubes, and the rounding threshold to be applied to the tube count calculation;

FIG. 5 shows a plate baffle displaying the tube configuration that results from applying the method described in the flow diagram shown in FIG. 4;

FIG. 6 shows an embodiment of a staggered ring heat exchanger tube configuration obtained using the method described in the flow diagram of FIG. 4;

FIG. 7 shows the velocity and flow field results from a computational fluid dynamic (CFD) simulation of a full-scale fluid heating system using a standard hexagonal ring heat exchanger tube configuration;

FIG. 8 shows the velocity field results from a computational fluid dynamic (CFD) simulation of a full-scale fluid heating system using the staggered ring heat exchanger tube configuration shown in FIG. 6;

FIG. 9 shows a photograph of a full-scale prototype of a fluid heating system incorporating the staggered ring heat exchanger tube configuration shown in FIG. 6;

FIG. 10 shows a plate baffle displaying the staggered ring heat exchanger tube configuration used in the full-scale prototype fluid heating system shown in FIG. 9.

DETAILED DESCRIPTION

There remains a need for fluid heating systems which provide more thermally compact designs, e.g., configurations that provide an increased ratio between the power and volume or footprint of the fluid heating systems (FHS), and which can be manufactured at a reasonable cost, with satisfactory material requirements, and reduced complexity. Improvements in the state-of-the-art for fluid heating system design, methods, and manufacture that enable increases in the thermal power achievable for a prescribed size or, conversely, enable a reduction in size for a prescribed thermal power level, accomplished for the same or lower manufacturing cost and complexity, are desirable.

It has been unexpectedly discovered that methods for reducing the size of fluid heating systems incorporating shell-and-tube heat exchangers achieved by increasing the bulk heat flux can exacerbate issues created by the non-uniform temperatures. Areas within the heat exchanger where heat is concentrated can lead to material failures, corrosion, and fouling. Where the temperature exceeds the boiling point of the production fluid, adverse effects may accumulate, particularly near structural joints or cracks that precipitate a production fluid phase change.

A fundamental objective in the design of a compact tube-and-shell heat exchanger for a fluid heating system is to determine an arrangement of a specific number of heat exchanger tubes in the smallest cross-sectional area while ensuring a production fluid temperature distribution that is as close to uniform as possible within prescribed design limits. Since the temperature distribution is partly determined by the production fluid flow field, in practical terms this means determining a tube arrangement and flow field so that the flow velocities in each fluid control volume around the heat exchanger tubes ensures a uniform opportunity for heat transfer. Regions where the flow velocity is too low (or where it may re-circulate) produce areas of high temperature since the dwell time near the heat exchanger tubes are too long, while regions where the flow velocity is too high implies too little time for heat transfer to occur across the heat transfer surfaces to the production fluid. Additionally, opportunities for the flow to go around heat exchanger elements, allowing for little or no exchange, rob flow from areas which need it. Different tube pattern geometries produce different production fluid flow patterns and velocity fields, and an important objective is to choose tube distribution patterns that, for a prescribed number of tubes, result in a relatively uniform cross-sectional temperature field produced by a flow field through an optimally-compact the tube arrangement that minimizes “hallways” (areas of high-velocity fluid flow resulting in incomplete heat-transfer) and stagnation zones (regions of low-velocity flow resulting in excessive temperature buildup).

Disclosed is a pattern for tube layout which is “staggered” relative to the direction of flow. Tube spacing is defined as the center-to-center arc length separation of consecutive tubes in the same radial row. Tube stagger is defined as the fraction of the tube spacing between two consecutive tubes that the tube centers are shifted in the same row where a tube stagger of zero indicates no shift and a tube stagger of one indicates that the row is shifted the full length of the tube separation distance. For the purposes of designing heat exchanger tube distribution patterns relative to the face of the tube sheets, the range of tube stagger is 1.0, or 0.99, or 0.98, or 0.97, or 0.96, or 0.95, or 0.94, or 0.93, or 0.92, or 0.91, or 0.90, or 0.85, or 0.80, or 0.75, or 0.70, or 0.65, or 0.6, or 0.55 to 0.5, or 0.45, or 0.4, or 0.35, or 0.3, or 0.25, or 0.20, or 0.15, or 0.10, or 0.09, or 0.08, or 0.07, or 0.06, or 0.05, or 0.04, or 0.03, or 0.02, or 0.01, or 0.00 wherein the foregoing upper and lower bounds can be independently combined. The range from 0.0 to 1.0 is specifically mentioned. The range from 0.01 to 0.99 is also specifically mentioned. The range from 0.1 to 0.9 is also specifically mentioned. In a symmetrical pattern, this means that a line connecting the centers of all tubes in a given row is perpendicular to the flow, and that each subsequent row is offset by a tube stagger, for example, one-half the tube spacing. Thus the passage between two consecutive tubes in a given row is all or partially occluded by another tube in the direction of the production fluid flow. This provides an improved amount of flow impingement and turning, which is responsible for enhancing turbulence, and raising heat transfer coefficients.

Furthermore, the magnitude of this effect is dependent upon constraints created by the tube diameter, the tube spacing, and the row spacing, and additionally can be quantified in terms of ratios of those parameters.

Heat exchangers which rely on cross flow can be rectangular in shape. However, there is an advantage in arranging heat exchangers into circular cross sections, as this allows the exchanger to exist within a shell of circular cross section. Having a shell with a circular cross section is not only labor and material efficient for construction, but it allows the shell to hold more pressure than flat planes arranged into a rectangular section and can have more compact overall physical dimensions.

Cross flow in circular sections is more challenging, as the flow needs to distribute as it makes its way across a tube bundle, then contracted again on the other side, as the chord which defined the flow area changes length as one moves across the diameter of a circle. This tends to create flow imbalance.

Methods for promoting a uniform velocity field within the flow of production fluid through the pressure vessel promote a uniform temperature distribution and efficient exchange of thermal energy across the walls of the heat exchanger tubes. Towards this end, it has also been unexpectedly discovered that radial and spiral flow of production fluid through the collection of heat exchanger tubes is effective at promoting a uniform, distribution of temperature and flow velocity within the heat exchanger. Radial flow of the production fluid can be arranged by design in a fluid heating system using arrangements of baffles that cause the flow to alternate between inward-directed radial flow towards the longitudinal axis and outward-directed radial flow towards the pressure vessel inner wall.

In preferable arrangements, which direct the flow radially, the flow can either be radially inward, or radially outward. As used herein, the term radially inward means that the fluid flow is from an outer edge of the tube arrangement inward towards a center point of the tube arrangement; and the term radially outward means that the fluid flow is from a center point of the tube arrangement outward towards an outer edge of the tube arrangement. In such cases the “flow area” is defined by the height of a section, and the circumference at each point. The typical staggered tube arrangement known to those skilled in the art of boiler and heat exchanger design are difficult to implement, as each row contains a different number of tubes.

Furthermore, the staggered tube arrangement typically results in “hexagonally shaped” patterns. These Hexagonal patterns, when placed in a radial flow arrangement, create alternating sections of aligned tubes, and staggered tubes. The result is that the pressure drop is not equally distributed among all radii, and thus most of the flow will proceed through the “aligned” sections, resulting in inefficient heat transfer overall, and more specifically the unit will experience high temperature zones on certain tubes, which could ultimately lead to heat exchanger failure.

Useful and novel methods for inducing radial production fluid flow in a heat exchanger and fluid heating system are described in the U.S. Provisional Application Ser. No. 62/281,534, filed on Jan. 21, 2016, “Baffle Assembly for a Heat Exchanger, Heat Exchanger Including a the Baffle Assembly, Fluid Heating System Including the Same, and Methods of Manufacture Thereof,” the content of which is incorporated herein by reference in its entirety. U.S. Provisional Application 62/281,534 describes methods for inducing radial production fluid flow using alternating plate and annular baffles.

Disclosed in FIG. 1 is a schematic of a fluid heating system 100. Ambient air is forced under pressure by a blower 102 through a conduit into a combustor 104, which comprises a furnace 106. In the furnace 106, a sustained combustion of a combination of fuel and air is maintained, releasing heat energy and combustion gases that travel through the upper tube sheet 105 and into a plurality of heat exchanger tubes 115. After traversing the heat exchanger tubes, the hot combustion gases pass through the lower tube sheet 110, into the exhaust plenum 112, and through the exhaust port to be conveyed out of the fluid heating system by an exhaust flue (not shown).

The production fluid is forced under pressure into an inlet 116, through the space 155 surrounding the heat exchanger tubes and out through the outlet 118. A baffle 108 can be placed such that the heat exchanger tubes traverse through the baffle to direct the flow of production fluid.

The capacity of the fluid heating system is total heat transferred from the thermal transfer fluid to the production fluid under standard conditions. By convention, when the production fluid consists of a liquid (e.g., water, thermal fluid, or thermal oil) the capacity is expressed in terms of British thermal units per hour (BTU/hr); and when the production fluid comprises a gas or vapor (e.g., steam) the standard unit of measurement is expressed in horsepower (HP). In an embodiment wherein the production fluid is a liquid (e.g., water, thermal fluid or thermal oil), the capacity of the fluid heating system may be between 100,000 BTU/hr, or 150,000 BTU/hr, or 200,000 BTU/hr, or 250,000 BTU/hr, or 300,000 BTU/hr, or 350,000 BTU/hr, or 400,000 BTU/hr, or 450,000 BTU/hr, or 500,000 BTU/hr, or 550,000 BTU/hr, or 600,000 BTU/hr to 50,000,000 BTU/hr, or 40,000,000 BTU/hr, or 30,000,000 BTU/hr, or 20,000,000 BTU/hr, or 15,000,000 BTU/hr, or 14,000,000 BTU/hr or 13,000,000 BTU/hr, or 12,000,000 BTU/hr, or 10,000,000 BTU/hr, 9,000,000 BTU/hr, 8,000,000 BTU/hr, or 7,000,000 BTU/hr wherein the foregoing upper and lower bounds can be independently combined.

An embodiment of a heat exchanger assembly where the plate and annular baffles alternate along the length of the heat exchanger to induce radial flow is shown in FIG. 2. In this embodiment three annular baffles 200 alternate with two plate baffles 210. The heat exchanger tubes sealingly pass through both types of baffles, and the annular baffles are sealed to the pressure vessel inner surface (not shown). As used herein, a plate baffle is a baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side is across a perimeter of the plate baffle. As used herein, an annular baffle is baffle that has a first side and an opposite second side, and wherein fluid communication between the first side and the second side of the annular baffle is through the annulus of the baffle.

The flow pattern induced by the alternating plate and annular baffles is illustrated in the rendering shown in FIG. 3, where production fluid entering the inlet 300 flows through the center region of the first annular baffle assembly 330, turns outward and flows radially outward 340 to the outer perimeter of the first plate baffle assembly 310 where it is turned radially inward to again flow radially to the center region of the second annular baffle assembly 320. This alternating radial flow pattern continues until the production fluid passes through the outlet (not shown) and out of the pressure vessel.

As is further discussed above, an advantage of the alternating plate and annular baffle system is that it can provide a more uniform production fluid flow field which is predominately radial, minimizing areas of high temperature that are understood to cause material failures, fluid boiling, and loss of thermal efficiency. The disclosed baffle assembly and heat exchanger provides for improvement in the management of production fluid flow of fluid heating systems and heat exchangers that enable greater compactness, reliability and performance in these systems.

It has been unexpectedly discovered that certain heat exchanger tube arrangements further promote the generation of uniform flow velocity and temperature fields in predominately radial production fluid flows. In contrast, it has been further discovered that conventional tube arrangements known to those skilled in the art of heat exchanger and boiler design: (a) are unable to fully exploit the benefits of radial production fluid flow, particularly where induced by alternating plate and annular baffle systems; (b) create extended hallways in the pressure vessel flow field where radial flow of production fluid does not impinge on heat exchange surfaces for significant distances, degrading the bulk heat transfer and creating regions of high-velocity flow; and, (c) fail to optimize the packing density of heat exchange surfaces within compact heat exchanger volumes.

In radial production fluid flows induced by alternating plate and annular baffle systems, regions of lower fluid velocity are located near the perimeter of the upper and lower tube sheets and the baffle assemblies; that is, in areas of the flow that are radially further from the heat exchanger longitudinal centerline. Conversely, regions of higher fluid velocity are located radially closer to the heat exchanger longitudinal centerline.

Standard tube configuration methods distribute the heat exchanger tubes in regular patterns; for example, in configurations where adjacent tubes are organized in equilateral triangles or squares, which produce regular polygonal configurations. Moreover, methods that produce regular polygonal tube configurations ignore the predominately circular symmetry of the fluid flow, leaving vertices and edges in the tube arrangements that cause local irregularities in the flow, temperature and velocity fields.

Disclosed is a method for optimizing the heat exchanger tube configuration that provides for one or both of: (a) capitalizes the advantages of production fluid radial and spiral flow and the structural tube configurations that result from applying the method; (b) reduces or eliminates extended straight, or nearly straight, paths (“hallways”) in the production fluid flow field near the heat exchange surfaces; improve or optimize the packing density of heat exchange surfaces within a design boundary for the collection of heat exchanger tubes. One aspect of the method and resulting tube configurations is that they are approximately circularly symmetric; that is, tubes are approximately configured in concentric rings relative to the heat exchanger longitudinal centerline. Tubes within a ring of diameter, D, relative to the longitudinal centerline are separated by a fixed radial tube Separation Angle (RA). The Separation Angle can be 0 to 180 degrees, or 1 to 179 degrees, or 1 to 90 degrees.

A second aspect of the disclosed method and the resulting tube configurations is that the tube arrangement is dense at radial distances further from the centerline and the tube density is sparse along the centerline.

A third aspect of the disclosed method and the resulting tube configuration is that the tube arrangement is staggered between adjacent rings. This ensures that radial fluid streamlines cannot travel far without impinging upon a heat transfer tube, thereby improving heat transfer, overall thermal efficiency and producing a more uniform radial flow and temperature field. This is accomplished by staggering tubes on adjacent rings, for example, from a first ring to an adjacent ring. More precisely, if T_(k)(i) denotes the i^(th) tube center on the k^(th) tube ring located at a distance D_(k)/2 from the centerline (for 1≦i≦N_(k), where N_(k) is the number of tubes on ring k), then the radial angle between T_(k)(1) and T_(k-1)(1) is the Index Angle for the k^(th) row, (IA_(k)). Alternatively, this is equivalent to rotating the k^(th) ring relative to ring k−1 by a ring-specific angle, IA_(k). The Index Angle can be 0 to 180 degrees, or 1 to 179 degrees, or 1 to 90 degrees.

A fourth aspect is that the disclosed method and resulting tube pattern improves or optimizes the packing density of the tube collection within a prescribed design boundary. This promotes increased bulk heat transfer of a compact heat exchanger. There are four, sometimes competing, measures of optimality.

Firstly, the alignment of tubes provides a measure of optimality measures how close to a staggered arrangement a given tube is, as compared to the two closest tubes in the next row. In a radial flow pattern, we can assume that the two closet tubes in the next row are simply the next two closest tube along the flow path, and do not necessarily need to be arranged in concentric rings, although the pattern presented here is indeed arranged on concentric rings.

Secondly, row-wise optimality is an indicator of how many consecutive rows, along one, or a narrow band of radii have low scoring staggering of the tubes. This seeks to ensure that tubes don't align to provide a single “hallway” which allows flow imbalance.

Thirdly, optimality of the stagger (or aligned) pattern provides a measure of optimality of the stagger pattern. Heat transfer is largely governed by Nusselt number, Nu, which, when evaluating Nu over a bank of tubes, the solution takes the form Nu=1.13C1Re^(m)Pr^(1/3). Evaluations of C1 and m have been conducted in academia, and tabulated results are available, and determined by two ratios: (a) SL/D, which is the ratio of distance between tube rows divided by the diameter of the tube, and (b) ST/D, which is the ratio of the tube spacing along a row divided by the diameter. There exists optimum combinations of both parameters. In general increasing SL will always result in lower values for C1. The effect of ST is less linear, and depends largely on the SL selected.

Fourthly, the packing fraction provides a measure of tube layout concerns packing fraction, or packing density, and is a measure of how many tubes can be fit inside a given area, specifically in this case, an area defined by a circle. Said another way, how large a circle is required to encompass all the tubes in a given tube bundle. In practical applications, the packing density must accommodate some of the constraints, calculated using the diameter of the tube, plus the minimum ligament distance, so that the packing fraction represents the full element size, with constraints, as opposed to being penalized for manufacturing considerations. Here, the meaning of “ligament distance” (or “ligament”) is the clearance required from the heat exchanger tube outside surface to allow for the structural attachment of the tube to the tube sheet (e.g., the clearance for a weld joint.).

The inventors have discovered a tube pattern and a method for specifying the pattern provided the required heat exchanger and boiler physical and performance requirements that is ideally suited for radial flow, in which the baffles which direct the flow exterior to the tubes are arranged such they direct the flow first from the center outward, in a radial sense, and then from the outer perimeter to the center in a radial sense.

Tube patterns for this flow regime need to provide roughly equal flow resistance across all radius line, in order to ensure that flow is balanced. In one embodiment, a tube pattern which is ideal for this flow consists of: (i) A plurality of N tubes are arranged in k concentric rings; (ii) the diameter of the tubes can be expressed as D; (iii) the minimum space between tubes is the ligament, and is expressed as l; (iv) the number of rings, k, is determined such that there is D+1 distance between the rings, guaranteeing that there will be at least l distance between any tubes in consecutive rings which land on the same radius line; (v) the distance from any tube on the outermost ring to the edge of the tube sheet is expressed as c; (vi) the tube sheet diameter can be expressed as D_(t). The outermost ring diameter can then be determined by D_(t)−D−2*c; (vii) all subsequent rings are then fully determined. Ring diameters can be expressed as RD_(k), where k indicates the ring number, with the first ring being the innermost ring; (viii) the maximum number of tubes on a given row is determined π*RD_(k)/(D+1). This value should be rounded down to the nearest whole number, so as not to compromise the ligament distance; (ix) one tube in each row is arbitrarily considered the “first tube”. Each first tube can be “clocked” by a number of degrees, a, as compared to horizontal plane when looking at a tubesheet. The maximum change in orientation is determined by the angle formed by two consecutive tubes in a single row; finally, each row of tubes is clocked by some α_(k) until optimality constraints are met or exceeded.

The number of tubes can vary, according to the design requirements, from 50 tubes to 1,000 tubes, or 75 tubes to 750 tubes, or 150 tubes to 600 tubes. The number of rings can be 2 rings to 100 rings, or 10 rings to 50 rings, or 5 rings to 20 rings. The tube diameter can vary from 0.5 cm to 30 cm, or 1 cm to 20 cm, or 1.25 cm to 6 cm. The diameter of the tube sheet can be 10 cm to 400 cm, or 20 cm to 200 cm, or 35 cm to 120 cm.

The circumference of the annular baffles is designed to be disposed on the inner surface of the pressure vessel and may be sealed by a weld or gasket (sealingly attached) or unsealed and mounted to the pressure vessel at attachment points. The annular opening is a major factor in specifying the fluid pressure drop in that heat exchanger section. It has been discovered that in typical embodiments the size of the annulus is appropriately chosen so that the first 1 to 3 inner rows of heat exchanger tubes pass through the annulus. Thus the dimensions of the annulus can be determined by the pressure drop characteristics of the flow through the annulus, and not a fixed fraction of the baffle surface, using methods known to practitioners skilled in the art. For plate baffles, the diameter is typically selected so that the outermost tube row sealingly passes through the plate baffle.

FIG. 4 shows a flow diagram for computing the tube Separation Angle (RA) and Index Angle (IA) for a tube configuration of concentric rings (indexed by the subscript, k). The method uses as input the design diameter, D_(t), of the tube configuration; the required gap, GAP, between the design diameter and the first (outermost) tube ring, the tube element clearance diameter which limits the closest separation distance between two adjacent tubes in a ring, CD_(k), required for each ring, k, of tubes; and a rounding threshold, RT, to be applied to the tube count to obtain integer values in the numerical rounding process.

An embodiment of tube configuration that results from the method detailed in FIG. 4 is shown in FIG. 5. The heat exchanger tubes within ring k are centered in a region defined by the clearance diameter, PD_(k), defined as diameter of the tube plus the Clearance (equivalently, ligament) which is the straight-line distance from tube edge to tube edge (OD). Tubes within a ring are separated by the ring separation angle, RA_(k), and are non-overlapping, for example, tubes 500 and 510 are located in an outermost ring and are separated by ring separation angle RA₁. The Radial Separation Angle varies from 0.1 degrees (0.1°), or 0.2°, or 0.3°, or 0.4°, or 0.5°, or 1°, or 2°, or 3°, or 4°, or 5°, or 6°, or 7°, or 8°, or 9°, or 10° to 180°, wherein the foregoing upper and lower bounds can be independently combined. The Radial Separation Angle Range of 0.5° to 180° is specifically mentioned. Tubes in two adjacent rows, k and k−1, are staggered rotating the two rings relative to each other by the ring-specific Index angle, IA_(k), for example, tubes 520 and 530 in ring 2 are separated from tubes 500 and 510 in ring 1 by Index angle IA₂ and Index angle IA₂, respectively.

FIG. 6 shows a plate baffle with a tube configuration produced using the method detailed in FIG. 4. The baffle is secured to the pressure vessel using mounting flanges 610 held into position by fasteners. The heat exchanger tube apparatus includes 274 heat exchanger tubes 600 arranged in nine concentric rings (1≦k≦9). In the outermost tube ring, each pair of adjacent tube centers are separated by a fixed, ring-specific separation angle; the ring separation angle for the outermost row (RA₁) is shown.

Improvement of the flow and temperature characteristics due to the optimized staggered tube configuration can be analyzed using computational fluid dynamic (CFD) simulation. FIG. 7 shows a CFD simulation under typical operating conditions for a hexagonal tube configuration. Note the region of high velocity located near the longitudinal centerline 700.

CFD simulation under the same operational conditions using a staggered tube configuration produced by the method detailed in FIG. 4 is shown in FIG. 8. Note the more spatially uniform velocity distribution, particularly near the longitudinal centerline 800.

A prototype fluid heating system incorporating a shell-and-tube heat exchanger with alternating plate and annular baffles and the staggered tube configuration produced by the method detailed in FIG. 4 was fabricated. A view of the heat exchanger is shown in FIG. 9 with the pressure vessel removed where a plate baffle assembly 900 and an annular baffle assembly 910 is visible. Heat exchanger tubes pass through the alternating sequence of plate and annular baffles assemblies, sealed by gaskets and held in place by retainers inducing a predominately radial flow pattern. FIG. 10. shows one of the plate baffles incorporated, displaying the staggered tube configuration. The fluid heating system was instrumented with temperature and flow sensors, and measurements of the flow velocity and temperature at various longitudinal locations were recorded and the enhanced thermal efficiency verified.

Set forth below are non-limiting embodiments of the present disclosure.

Embodiment 1

A heat exchanger tube assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, wherein adjacent tubes on a ring are separated by a radial separation angle RA.

Embodiment 2

The heat exchanger tube assembly of embodiment 1, wherein the radial separation angle is 1 to 90 degrees.

Embodiment 3

The heat exchanger tube assembly of any one or more of the preceding embodiments, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 4

The heat exchanger tube assembly of any one or more of the preceding embodiments, further comprising a baffle located between the first tube sheet and the second tube sheets, wherein the plurality of heat exchanger tubes traverses through the baffle.

Embodiment 5

The heat exchanger tube assembly of embodiment 4, wherein the baffle comprises at least one plate baffle; wherein fluid communication between a first side and a second side of the plate baffle is across a perimeter of the plate baffle.

Embodiment 6

The heat exchanger tube assembly of any one or more of embodiments 4 to 5, wherein the baffle comprises at least one annular baffle; wherein fluid communication between a first side and a second side of the annular baffle is through the annulus of the baffle.

Embodiment 7

The heat exchanger tube assembly of any one or more of embodiments 4 to 6, wherein the baffle comprises at least two plate baffles and at least two annular baffles; wherein a fluid flow traverses an alternating path of plate baffles and annular baffles.

Embodiment 8

The heat exchanger tube assembly of any one or more of the preceding embodiments, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 9

A heat exchanger comprising: a pressure vessel; and the heat exchanger tube assembly of any one or more of the preceding embodiments; wherein the heat exchanger tube assembly is disposed in the pressure vessel.

Embodiment 10

The heat exchanger of embodiment 9, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 11

A fluid heating system comprising: the heat exchanger of any one or more of embodiments 9 to 10; wherein the pressure vessel comprises a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.

Embodiment 12

The heat exchanger tube assembly of embodiment 11, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.

Embodiment 13

A method of calculating the radial separation angle RA, and the radial stagger index angle IA, for a staggered ring heat exchanger tube configuration, for example, of any one or more of the preceding embodiments, using the design diameter DD of the tube configuration, a gap GAP between the design diameter and the first tube ring, the tube element clearance diameter CD_(k) for each row k of tubes, and the rounding threshold RT to be applied to the tube count, the method comprising: computing a diameter of an outer row RD₁ using the Formula 1 RD₁=DD−(2×GAP)−CD₁; (1) computing the diameter RDk of the interior rows 2≦k using the Formula 2 RDk=RDk−1−CDk−1−CDk (2) for each row diameter where RDk≧0; computing the tube count for each row k using Formula 3 CTk=360/2 sin−1(CDk/RDk); (3) computing the integer tube count by rounding using the rounding threshold RT, where RT is between 0.001 and 0.99, wherein: if the fractional part of the computed tube count CTk is greater than the rounding threshold RT, round the tube count using Formula 4 Ck=ceil(CTk), (4), and compute the final ring diameter using Formula 5 Dk=CDk/sin(360/2Ck); (5) otherwise round the tube count using Formula 6 Ck=floor(CTk), and (6) compute the final ring diameter using Formula 7 D1=OD−(2×GAP)−CD1 (8) if the computation is for the first row or Formula 9 Dk=Dk−1−CDk−1−CDk (9) if for an inner row with k>1; computing the fixed row separation angle RAk for tubes in each row from k=1 to the innermost row using Formula 10 RAk=360/Ck; (10) computing the fixed tube stagger index angle IAk for adjacent tubes in adjacent rows, k and k−1, using Formula 11 IAk=(RAk+RAk−1)/2 (11) for each inner row and setting IA1=0 for the first row, k=1.

Embodiment 14

A heat exchanger tube assembly for example, of any one or more of the preceding embodiments, comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, the heat exchange tubes in each ring have approximately the same tube diameter and ligament; the radial distance separating two adjacent rings is between one half and three times the sum of the minimum ligament and minimum tube diameter for any tube on the two adjacent rings; wherein adjacent tubes on a ring are separated by a radial separation angle between 0.5 degrees and 180 degrees; and each concentric ring contains a designated first tube.

The disclosure has been described with reference to the accompanying drawings, in which various embodiments are shown. This disclosure may, however, be embodied in many different forms, and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like reference numerals refer to like elements throughout.

It will be understood that when an element is referred to as being “on” another element, it can be directly on the other element or intervening elements may be present there between. In contrast, when an element is referred to as being “directly on” another element, there are no intervening elements present. Also, the element may be on an outer surface or on an inner surface of the other element, and thus “on” may be inclusive of “in” and “on.”

It will be understood that, although the terms “first,” “second,” “third,” etc. may be used herein to describe various elements, components, regions, layers, and/or sections, these elements, components, regions, layers, and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer, or section from another element, component, region, layer or section. Thus, “a first element,” “component,” “region,” “layer,” or “section” discussed below could be termed a second element, component, region, layer, or section without departing from the teachings herein.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms, including “at least one,” unless the content clearly indicates otherwise. “Or” means “and/or.” As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. It will be further understood that the terms “comprises” and/or “comprising,” or “includes,” and/or “including” when used in this specification, specify the presence of stated features, regions, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, regions, integers, steps, operations, elements, components, and/or groups thereof.

Furthermore, relative terms, such as “lower” or “bottom” and “upper” or “top,” may be used herein to describe one element's relationship to another element as illustrated in the Figures. It will be understood that relative terms are intended to encompass different orientations of the device in addition to the orientation depicted in the Figures. For example, if the device in one of the figures is turned over, elements described as being on the “lower” side of other elements would then be oriented on “upper” sides of the other elements. The exemplary term “lower,” can therefore, encompasses both an orientation of “lower” and “upper,” depending on the particular orientation of the figure. Similarly, if the device in one of the figures is turned over, elements described as “below” or “beneath” other elements would then be oriented “above” the other elements. The exemplary terms “below” or “beneath” can, therefore, encompass both an orientation of above and below.

Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

Exemplary embodiments are described herein with reference to cross section illustrations that are schematic illustrations of idealized embodiments. As such, variations from the shapes of the illustrations as a result, for example, of manufacturing techniques and/or tolerances, are to be expected. Thus, embodiments described herein should not be construed as limited to the particular shapes of regions as illustrated herein but are to include deviations in shapes that result, for example, from manufacturing. For example, a region illustrated or described as flat may, typically, have rough and/or nonlinear features. Moreover, sharp angles that are illustrated may be rounded. Thus, the regions illustrated in the figures are schematic in nature and their shapes are not intended to illustrate the precise shape of a region and are not intended to limit the scope of the present claims. 

What is claimed is:
 1. A heat exchanger tube assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, wherein adjacent tubes on a ring are separated by a radial separation angle RA.
 2. The heat exchanger tube assembly of claim 1, wherein the radial separation angle is 1 to 90 degrees.
 3. The heat exchanger tube assembly of claim 1, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.
 4. The heat exchanger tube assembly of claim 1, further comprising a baffle located between the first tube sheet and the second tube sheets, wherein the plurality of heat exchanger tubes traverses through the baffle.
 5. The heat exchanger tube assembly of claim 4, wherein the baffle comprises at least one plate baffle; wherein fluid communication between a first side and a second side of the plate baffle is across a perimeter of the plate baffle.
 6. The heat exchanger tube assembly of claim 4, wherein the baffle comprises at least one annular baffle; wherein fluid communication between a first side and a second side of the annular baffle is through the annulus of the baffle.
 7. The heat exchanger tube assembly of claim 4, wherein the baffle comprises at least two plate baffles and at least two annular baffles; wherein a fluid flow traverses an alternating path of plate baffles and annular baffles.
 8. The heat exchanger tube assembly of claim 4, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.
 9. A heat exchanger comprising: a pressure vessel; and the heat exchanger tube assembly of claim 1; wherein the heat exchanger tube assembly is disposed in the pressure vessel.
 10. The heat exchanger of claim 9, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.
 11. A fluid heating system comprising: the heat exchanger of claim 9; wherein the pressure vessel comprises a pressure vessel shell comprising a first inlet and first outlet, a shell, a first top head and a first bottom head, wherein the shell is disposed between the first top head and the first bottom head, and wherein the first inlet and the first outlet are each independently on the shell, the first top head, or the first bottom head; a conduit, which penetrates the pressure vessel shell, wherein a first end of the conduit is connected to the first tube sheet wherein the conduit is in fluid communication with the heat exchanger tubes and wherein a second end of the conduit is on the outside of the pressure vessel shell; a burner disposed in the conduit; and a blower, which is in fluid communication with the second end of the conduit.
 12. The heat exchanger tube assembly of claim 11, wherein neighboring tubes on adjacent rings are separated by rotating all the tubes within an inner ring by a radial index angle, IA, relative to the next outermost tube ring.
 13. A method of calculating the radial separation angle RA, and the radial stagger index angle IA, for a staggered ring heat exchanger tube configuration, using the design diameter DD of the tube configuration, a gap GAP between the design diameter and the first tube ring, the tube element clearance diameter CD_(k) for each row k of tubes, and the rounding threshold RT to be applied to the tube count, the method comprising: computing a diameter of an outer row RD₁ using the Formula 1 RD₁=DD−(2×GAP)−CD₁;  (1) computing the diameter RD_(k) of the interior rows 2≦k using the Formula 2 RD_(k)=RD_(k-1)−CD_(k-1)−CD_(k)  (2) for each row diameter where RD_(k)≧0; computing the tube count for each row k using Formula 3 CT_(k)=360/2 sin⁻¹(CD_(k)/RD_(k));  (3) computing the integer tube count by rounding using the rounding threshold RT, where RT is between 0.001 and 0.99, wherein: if the fractional part of the computed tube count CT_(k) is greater than the rounding threshold RT, round the tube count using Formula 4 C _(k)=ceil(CT_(k)),  (4), and compute the final ring diameter using Formula 5 D _(k)=CD_(k)/sin(360/2C _(k));  (5) otherwise round the tube count using Formula 6 C _(k)=floor(CT_(k)), and  (6) compute the final ring diameter using Formula 7 D ₁=OD−(2×GAP)−CD₁  (8) if the computation is for the first row or Formula 9 D _(k) =D _(k-1)−CD_(k-1)−CD_(k)  (9) if for an inner row with k>1; computing the fixed row separation angle RA_(k) for tubes in each row from k=1 to the innermost row using Formula 10 RA_(k)=360/C _(k);  (10) computing the fixed tube stagger index angle IA_(k) for adjacent tubes in adjacent rows, k and k−1, using Formula 11 IA_(k)=(RA_(k)+RA_(k-1))/2  (11) for each inner row and setting IA₁=0 for the first row, k=1.
 14. A heat exchanger tube assembly comprising: a first tube sheet; a second tube sheet opposite the first sheet; a plurality of heat exchanger tubes, wherein each heat exchanger tube of the plurality of heat exchanger tubes independently connects the first tube sheet and the second tube sheet, and wherein the heat exchanger tubes are in a staggered ring configuration that comprises a plurality of concentric rings of tubes, the heat exchange tubes in each ring have approximately the same tube diameter and ligament; the radial distance separating two adjacent rings is between one half and three times the sum of the minimum ligament and minimum tube diameter for any tube on the two adjacent rings; wherein adjacent tubes on a ring are separated by a radial separation angle between 0.5 degrees and 180 degrees; and each concentric ring contains a designated first tube. 